Problem: Divide the following complex numbers: $\dfrac{4(\cos(\frac{3}{4}\pi) + i \sin(\frac{3}{4}\pi))}{2(\cos(\frac{5}{12}\pi) + i \sin(\frac{5}{12}\pi))}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Answer: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $4(\cos(\frac{3}{4}\pi) + i \sin(\frac{3}{4}\pi))$ ) has angle $\frac{3}{4}\pi$ and radius 4. The second number ( $2(\cos(\frac{5}{12}\pi) + i \sin(\frac{5}{12}\pi))$ ) has angle $\frac{5}{12}\pi$ and radius 2. The radius of the result will be $\frac{4}{2}$ , which is 2. The angle of the result is $\frac{3}{4}\pi - \frac{5}{12}\pi = \frac{1}{3}\pi$ The radius of the result is $2$ and the angle of the result is $\frac{1}{3}\pi$.